# Depinning asymptotics in ergodic media

Source: [Depinning asymptotics in ergodic media](<https://www.sota2.com/research/paper/68fa353d1e209131ce89fe53>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T21:09:19.321Z

Authors: Arnd Scheel, Sergey Tikhomirov

Published: 2016-10-22T23:03:35.000Z

## Abstract

We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent depending a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are satisfied in a context of weak inhomogeneity of the medium and almost balanced kinetics, and compare asymptotics with numerical simulations.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1610.07102>)

[PDF](<https://arxiv.org/pdf/1610.07102.pdf>)